Mutexes are used to help determine when a belief state is unreachable.
Mutexes improve the pruning power of heuristics by accounting for negative interactions.
The mutexes are only used to improve our heuristics,
so it is reasonable to compute only a subset of the mutexes.
We would like to know which mutexes are the most cost effective because
the number of possible mutexes we can find is quite
large.

We can use several schemes to compute a subset of the mutexes. The
schemes combine different types of mutexes with types of cross-world
checking. The mutex types are: computing no mutexes (NX), computing
only static interference mutexes (StX), computing (StX) plus
inconsistent support and competing needs mutexes - dynamic mutexes
(DyX), and computing (DyX) plus induced mutexes - full mutexes
(FX). The cross-world checking (see appendix B) reduction schemes
are: computing mutexes across same-worlds (SX) and computing mutexes
across pairs of worlds in the intersection (conjunction) of element
labels (IX).

Table 4:
Results for CAltAlt using
with mutex schemes. The data is Graph Construction Time (ms)/All
Other Time (ms)/# Expanded Nodes, ``TO'' indicates a time out (20
minutes) and ``-'' indicates no attempt.

Table 4 shows that within CAltAlt, using the relaxed plan
heuristic and changing the way we compute mutexes on the
can
drastically alter performance. Often, the cross-world mutexes are so
numerous that building the
takes too much time. To see if we
could reduce graph construction overhead without hindering
performance, we evaluated
when the LUG is built (a)
considering all cross-world relations, for the schemes (NX), (StX),
(DyX), and (FX); and (b) same-world relations for the schemes
(DyX-SX) and (FX-SX), and (c) cross-world relations for all possible
worlds pairs in the intersection of element's labels (DyX-IX) and
(FX-IX).

The results show that simpler problems like BT and BTC do not
benefit as much from advanced computation of mutexes beyond static
interference. However, for the Rovers and Logistics problems,
advanced mutexes play a larger role. Mainly, interference,
competing needs, and inconsistent support mutexes are important. The
competing needs and inconsistent support mutexes seem to have a
large impact on the informedness of the guidance given by the
,
as scalability improves most here. Induced mutexes don't improve
search time much, and only add to graph computation time. A possible
reason induced mutexes don't help as much in these domains is that
all the actions have at most two effects, an unconditional and
conditional effect. Reducing cross-world mutex checking also helps
quite a bit. It seems that only checking same-world mutexes is
sufficient to solve large problems. Interestingly, the
graphs
compute same-world interference, competing needs, and inconsistent
support mutexes within each graph, equating to the same scenario as
(DyX-SX), however, the LUG provides a much faster construction time,
evidenced by the
's ability to out-scale
.